Expanding Search Box in Genesis. http://sridharkatakam.com/expanding-search-box-genesis/

gistfile1.php

//* Make Font Awesome available
add_action( 'wp_enqueue_scripts', 'enqueue_font_awesome' );
function enqueue_font_awesome() {

	wp_enqueue_style( 'font-awesome', '//netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css' );

}

//* Customize search form input box text
add_filter( 'genesis_search_text', 'sp_search_text' );
function sp_search_text( $text ) {
	return esc_attr( 'Search' );
}

//* Customize search form input button text
add_filter( 'genesis_search_button_text', 'sk_search_button_text' );
function sk_search_button_text( $text ) {

	return esc_attr( '' );

}

gistfile2.css

input:focus::-webkit-input-placeholder { color:transparent; }
input:focus:-moz-placeholder { color:transparent; } /* Firefox 18- */
input:focus::-moz-placeholder { color:transparent; } /* Firefox 19+ */
input:focus:-ms-input-placeholder { color:transparent; } /* oldIE ;) */

.genesis-nav-menu .search-form input[type="search"] {
	padding-right: 3rem;
	-moz-transition: 400ms width ease;
    -webkit-transition-duration: 400ms;
    -webkit-transition-property: width;
    -webkit-transition-timing-function: ease;
    -o-transition-duration: 400ms;
    -o-transition-property: width;
    -o-transition-timing-function: ease;
    width: 92px;
}

.genesis-nav-menu .search-form input[type="search"]:focus {
	width: 189px;
}

.search-form {
	position: relative;
}

.search-form input[type="submit"] {
	position: absolute;
	font-family: FontAwesome;
	clip: inherit;
	width: 16px;
	height: 16px;
	background: transparent;
	color: #999;
	right: 10px;
	top: 18px;
}

.search-form input[type="submit"]:hover {
	color: #F15123;
}

gistfile3.php

//* Add a right aligned search form in Secondary Navigation
add_filter( 'genesis_nav_items', 'sk_search_form', 10, 2 );
add_filter( 'wp_nav_menu_items', 'sk_search_form', 10, 2 );

function sk_search_form($menu, $args) {
	$args = (array)$args;
	if ( 'secondary' !== $args['theme_location']  )
		return $menu;
	ob_start();
	get_search_form();
	$search_form = ob_get_clean();
	return $menu . '<li class="right">' . $search_form . '</li>';
}

gistfile4.css

.menu-secondary > .right {
	padding: 0;
	margin-top: 1.4rem;
}

gistfile5.php

//* Enqueue Dashicons
add_action( 'wp_enqueue_scripts', 'enqueue_dashicons' );
function enqueue_dashicons() {

	wp_enqueue_style( 'dashicons' );

}

//* Customize search form input box text
add_filter( 'genesis_search_text', 'sp_search_text' );
function sp_search_text( $text ) {
	return esc_attr( 'Search' );
}

//* Customize search form input button text
add_filter( 'genesis_search_button_text', 'sk_search_button_text' );
function sk_search_button_text( $text ) {

	return esc_attr( '' );

}

gistfile6.css

.search-form input[type="submit"] {
	position: absolute;
	display: inline-block;
	-webkit-font-smoothing: antialiased;
	font: normal 20px/1 'dashicons';
	vertical-align: top;
	clip: inherit;
	width: 20px;
	height: 20px;
	background: transparent;
	color: #999;
	right: 10px;
	top: 18px;
}